Simple 2D random diffusion question (collisions with wall)

I am looking at an object that diffuses randomly inside a circular plane.What is the easiest way to find the expectation value for how long would it take on average to reach the wall if it was initially placed at a random position?

If it is easier: what if the initial position were the center of the circle?

I can find the radius of the plane and the diffusion rate.

The object in reality diffuses continuously, not in discrete steps.

This is quite an annoying recurring problem for me at the moment, any help would be greatly appreciated.